Evidence from epidemiological and medical research is often central to major policy decisions. Modern research data have become increasingly complex, raising non-traditional modeling and inferential challenges. In particular, advancements in technology and computation have made recording and processing of functional data possible. Some examples of functional data are time series of electroencephalographic (EEG) activity, anatomical shape, and functional MRI. In this context it has become increasingly necessary to adapt existent tools and design new statistical methods to extract information without stringent parametric assumptions about the population or subject functional characteristics. The purpose of this proposal is to develop classes of statistical models for feature extraction from single-level (one or multiple functions per subject at one visit) and multilevel (one or multiple functions per subject at multiple visits) functional data having a large number of subjects and large within- and between-subject heterogeneity. Specifically, we are motivated by our ongoing studies of the association of sleep and adverse health outcomes. PUBLIC HEALTH RELEVANCE the major benefits of these studies to public health will be to increase our knowledge concerning the effects of sleep on health outcomes. Development of methods to better understand the sleep architecture in the general population will allow further determination of how medical disorders may disturb sleep and whether sleep disruption is related to health-related consequences. The methodology proposed is very general and will impact many other areas of scientific research. Two examples of scientific data that would directly benefit from the proposed research are Magnetic Resonance Imaging (MRI) of the brain, heart, etc. and daily blood glucose trajectories recorded at multiple visits.